# SIX. Dealing with Unequal Variance Around the Regression Line

1. Mari Palta

Published Online: 11 AUG 2003

DOI: 10.1002/0471467979.ch6

## Quantitative Methods in Population Health: Extensions of Ordinary Regression

#### How to Cite

Palta, M. (2003) Dealing with Unequal Variance Around the Regression Line, in Quantitative Methods in Population Health: Extensions of Ordinary Regression, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471467979.ch6

#### Publication History

1. Published Online: 11 AUG 2003
2. Published Print: 15 AUG 2003

#### Book Series:

1. Wiley Series in Probability and Statistics

#### Book Series Editors:

1. Walter A. Shewhart and
2. Samuel S. Wilks

#### ISBN Information

Print ISBN: 9780471455059

Online ISBN: 9780471467977

## SEARCH

### Keywords:

• unequal variance;
• unbiasedness;
• empirical standard errors;
• PROC MIXED;
• functional transformation;
• elasticity;
• efficiency;
• weighted least squares;
• model based standard errors;
• linear transformation

### Summary

We demonstrate that the ordinary least squares estimator is unbiased even with unequal variance. The effect of unequal variance on the derivation of the variance of ordinary regression estimators is pointed out. The use of the empirical (robust or Huber) estimator is introduced as a solution to obtaining correct standard errors. Empirical estimator obtained by PROC MIXED. Examples of applying empirical option to regressions of glycosylated hemoglobin on age and of systolic blood pressure on age, BMI and gender.

The functional transformation approach is introduced as one approach to unequal variance. An approximate formula is given for choosing the transformation. Example of regressing inverse of GHb on diabetes duration. Log of outcome on log of predictor regression is discussed and interpreted as elasticity. Example of the cost of medical care on gender and BMI.

Weighted least squares derived from linear transformation to obtain efficient estimators. Unbiasedness of weighted least squares estimators is demonstrated. Model based and empirical standard errors are derived. Weighted least squares are applied by PROC REG and PROC MIXED to regression of GHb on diabetes duration.